Triple
T3214179
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fibonacci sequence |
E67350
|
entity |
| Predicate | hasClosedForm |
P46241
|
FINISHED |
| Object |
Binet’s formula
Binet’s formula is the closed-form expression that computes the nth Fibonacci number using powers of the golden ratio and its conjugate.
|
E67350
|
NE FINISHED |
How this triple was built (5 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Binet’s formula | Statement: [Fibonacci sequence, hasClosedForm, Binet’s formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Binet’s formula Context triple: [Fibonacci sequence, hasClosedForm, Binet’s formula]
-
A.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
C.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
E.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Binet’s formula Triple: [Fibonacci sequence, hasClosedForm, Binet’s formula]
Generated description
Binet’s formula is the closed-form expression that computes the nth Fibonacci number using powers of the golden ratio and its conjugate.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Binet’s formula Target entity description: Binet’s formula is the closed-form expression that computes the nth Fibonacci number using powers of the golden ratio and its conjugate.
-
A.
Fibonacci sequence
chosen
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
-
C.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
E.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
- F. None of above.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasClosedForm Context triple: [Fibonacci sequence, hasClosedForm, Binet’s formula]
-
A.
hasSymbolicForm
Indicates that one entity serves as the symbolic representation or abstract form of another entity.
-
B.
hasFullForm
Indicates that one entity is the complete, expanded, or unabbreviated form of another entity.
-
C.
admitsSolution
Indicates that a problem, system, or situation allows for or possesses at least one valid solution.
-
D.
hasFormulation
Indicates that one entity is expressed, prepared, or configured in a particular form or composition defined by another entity.
-
E.
hasNonStandardForm
Indicates that an entity possesses a form, variant, or representation that deviates from the standard, canonical, or commonly accepted form.
- F. None of above. chosen
Provenance (7 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69ad858ac36c81909962589cd277d6e2 |
completed | March 8, 2026, 2:19 p.m. |
| NER | Named-entity recognition | batch_69adaabd01d48190be0dc610b9987a25 |
completed | March 8, 2026, 4:58 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b26237211c81908cddc4e8d42e497e |
completed | March 12, 2026, 6:50 a.m. |
| NEDg | Description generation | batch_69b264c54c508190be85da879935e7f4 |
completed | March 12, 2026, 7:01 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69b268d60bd0819097194da2e9065947 |
completed | March 12, 2026, 7:18 a.m. |
| PD | Predicate disambiguation | batch_69ad9e09b83881908801d79c3d9254f9 |
completed | March 8, 2026, 4:04 p.m. |
| PDg | Predicate description generation | batch_69ada0f9259c8190afbc5ad0fa55436b |
completed | March 8, 2026, 4:16 p.m. |
Created at: March 8, 2026, 3:07 p.m.